MPEG-LA does not. https://www.mpegla.com/programs/avc-h-264/ is their license scheme - while they allow a certain threshold below which cutoff isn't required, there's a lot of companies (such as Blizzard Entertainment!) whose primary distributed product is solely for video playback. H.264 requires a license for personal, at-home playback of encoded files. You have such a license if you have a Windows OS, an Apple OS, if you're using Chrome, or if you use a set-top box, or other "single-use" device which can play back H.264. You do not have such a license on linux with mplayer.
They make money licensing IP to hardware manufacturers.